Along with the development of modern communication technologies, increasing attention has been paid to various nonlinear characteristics of power amplifiers, and the behavior model has also become a research focus in the field of microwave circuits. As compared with the traditional transistor-level circuit model, the analysis and the calculation in the behavior model has been greatly simplified while maintaining sufficient precision of the analysis of a nonlinear circuit, so the behavior model is particularly applicable to the analysis of performance of a broadband digital signal system, and thus expected to have a good application prospective in the researches on large-scale integrated circuits and pre-distortion technologies. The memory effect of the power amplifier has to be taken into account for the broadband communication system, so the traditional nonlinear model will not be applicable any longer. Currently the dynamic characteristic of the power amplifier is typically described using a memory-enabled polynomial, an artificial neural network, or another model. As compared with the behavior model based upon the artificial neural network, the modified Volterra series model can describe the physical definition of the nonlinear system more clearly, but the number of parameters for the model thereof increases exponentially with the increasing nonlinearity and memory length of the system, so the model can only be applicable to the research on a weakly-nonlinear system; otherwise, the model may suffer from the problem of calculation convergence.
There is a very serious memory effect of the power amplifier for a ultra-broadband signal according to inconsistent responses of the power amplifier to the signal at respective frequencies so that a signal output by the power amplifier is dependent upon both the signal at the current instance of time, and the preceding instance of time to the power amplifier, and apparently the memory depth of the power amplifier significantly increases with the increasing bandwidth of the signal. The power amplifier which is an analog device is a nonlinear system with nonlinear distortion of Amplitude Modulation-Amplitude Modulation (AM-AM) and Amplitude Modulation-Phase Modulation (AM-PM), where the AM-AM distortion refers to distortion in amplitude of an output signal relative to an input signal, for example, if the amplitude of the input signal drops below threshold voltage or rises above saturation voltage, then the output voltage signal may be clamped or capped, i.e., AM-AM distortion. The AM-PM distortion refers to that the difference in potential between the output signals and input signals varies with the varying amplitude of the input signal of the nonlinear power amplifier. If a narrow-band signal is input, then there will be such an insignificant influence of the memory effect that the AM-AM and AM-PM distortions of the power amplifier can be corrected for a better effect. As the bandwidth of the signal is increasing, particularly an ultra-broadband signal of 100 M in next-generation mobile communication, the memory effect of the power amplifier may be so serious that the power amplifier becomes a very complex system including both linear distortions and nonlinear distortions, and a theoretical complete expression of such a system is the modified Volterra series. Apparently the modified Volterra series is currently impractical and has to be simplified and optimized, and how to extract a dominating distortion model of the power amplifier, and to create a working, practicable, and low-overhead pre-distortion model of the power amplifier is a very challenging job.
In order to address this problem, the behavior model of the amplifier is typically created in recent years using some simplified models including the common Wiener model and Hammerstein model, where both of the models are greatly reduced in complexity and can be applicable to a strongly-nonlinear system, so they have been widely applied in the research on the nonlinear behavior model of the power amplifier. However these two models can not describe comprehensively the nonlinear characteristic of the power amplifier, and particularly can not define precisely the envelope memory effect of the power amplifier; and moreover neither Wiener model nor the Hammerstein model is a linear equation to be solved for the parameters of the models, making it difficult to extract the parameters of the model. The Memory Polynomial (MP) is another common behavior model which can be regarded as an extended Hammerstein model, but the required precision of the model may not be achieved. Accordingly it is desirable to create a more precise behavior model with linear parameters.